SOLUTION: Two cars are 200 miles apart and traveling towards each other on the same road. They meet in 2 hours. One car is traveling 4 mph. faster than the other car. What is the speed of ea

Question 896280: Two cars are 200 miles apart and traveling towards each other on the same road. They meet in 2 hours. One car is traveling 4 mph. faster than the other car. What is the speed of each car? (Directions for problem: Write as an equation. Don't solve!)
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the distance between them is 200 miles.
the first car travels x miles.
the second car travels 200 - x miles which is the difference between 200 and x.
they meet somewhere in the middle.

they both travel for 2 hours.
the rate of the first car is y
the rate of the second car is y - 4 because the first car is traveling 4 miles per hour faster than the second car.

you have:

first car travels x miles at a rate of y miles per hour.
second car travels 200 - x miles at a rate of y - 4 miles per hour.

they both travel for 2 hours.

rate * time = distance.

for the first car this becomes y * 2 = x
for the second car this becomes (y-4) * 2 = (200-x)

from the equation for the first car, you get x = y*2
you can replace x in the equation for the second car by y*2 and then solve for y.

you get:

(y-4) * 2 = (200 - x) becomes (y-4) * 2 = (200 - y*2)

that's your equation.

solve for y and you get your answer.

you should get the first car is traveling at 52 miles per hour and the second car is traveling at 48 miles per hour.

you can then solve for the distance and you should get the first car has traveled 104 miles and the second car has traveled 96 miles.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Two cars are 200 miles apart and traveling towards each other on the same road. They meet in 2 hours. One car is traveling 4 mph. faster than the other car. What is the speed of each car? (Directions for problem: Write as an equation. Don't solve!)

Let speed of slower car, be S
Then speed of faster car is: S + 4
Since it takes 2 hours for them to meet and they'll both cover 200 miles, then we can say that:
2(S) + 2(S + 4) = 200

Solve this for S, the speed of the slower car, and add 4 to that result to get the speed of the faster car.
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